Problem: Solve for $r$, $ \dfrac{7}{25r} = -\dfrac{8}{10r} + \dfrac{5r + 2}{5r} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $25r$ $10r$ and $5r$ The common denominator is $50r$ To get $50r$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{7}{25r} \times \dfrac{2}{2} = \dfrac{14}{50r} $ To get $50r$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ -\dfrac{8}{10r} \times \dfrac{5}{5} = -\dfrac{40}{50r} $ To get $50r$ in the denominator of the third term, multiply it by $\frac{10}{10}$ $ \dfrac{5r + 2}{5r} \times \dfrac{10}{10} = \dfrac{50r + 20}{50r} $ This give us: $ \dfrac{14}{50r} = -\dfrac{40}{50r} + \dfrac{50r + 20}{50r} $ If we multiply both sides of the equation by $50r$ , we get: $ 14 = -40 + 50r + 20$ $ 14 = 50r - 20$ $ 34 = 50r $ $ r = \dfrac{17}{25}$